Promise to support father, keeping nothing and do without (8)
I believe the answer is:
forswear
'do without' is the definition.
(thesaurus)
'promise to support father keeping nothing' is the wordplay.
'promise' becomes 'swear' (as in swearing something is true).
'to support' means one lot of letters go next to another (in a down clue, some letters hold others up).
'father' becomes 'fr' (abbreviation as in a priest's title).
'keeping' means one lot of letters goes inside another (some letters kept inside).
'nothing' becomes 'O' (O resembles 0).
'fr' going around 'o' is 'for'.
'swear' put after 'for' is 'FORSWEAR'.
'and' acts as a link.
(Other definitions for forswear that I've seen before include "Deny on oath" , "Denounce" , "Renounce upon oath - far worse (anag)" , "Give up" , "Reject or disavow" .)